Professors at state universities are unique among state employees:
"Outside the university, the state must maintain neutrality toward the content of speech, cannot dictate what is true or false, and cannot compel speech. In the classroom, by contrast, professors routinely regulate what can be discussed, are paid to distinguish between truth and falsehood, and often require students to argue particular viewpoints for pedagogical purposes. [...] Thus even a public university, which is bound by the First Amendment, must have leeway to judge and control speech in ways that other government entities do not."
"The Supreme Court has ruled that most public employees speech rights must bow to the state employer's need to control the speech of its workforce. When a public employee speaks in her official capacity, for example, she has no First Amendment rights, because she is effectively speaking for the government. Her boss can tell her what to say and what not to say. Only when she speaks as a private citizen and only when she addresses 'a matter of public concern' is her speech protected by the First Amendment."
Yet this "cannot be the rule for public university professors. When they teach their classes, conduct research, or write papers, they are acting in their capacity as government employees. Yet no one thinks they are expressing the government's message.* And for academic work to be legitimate, professors must have the freedom to follow the evidence and logic wherever they may lead. For this reason, when the Supreme Court ruled that the First Amendment does not protect most government employees' on-the-job speech, it expressly noted that a different rule might apply to public university professors, and many lower courts have held that those professors' on-the-job speech is protected."
*- Put another way: "[N]o one thinks that professors in a public university are expressing the government's message in their classrooms or scholarship, They are not press secretaries."